A function y =f(x) defined for all x 1 satisfies all of the following conditions: (i) f '(x) 1; f'(x) >0 forx 0 forx 1; f "(-1) =0; f "(1) is not defined. (iii) lim, - f(x) = -0, lim, 1+ f(x) = 00; limr-4-0% f(a) = -2, lime-+0% f(@) = -00. (iv) f(2) = f(0) =0, f(-1) = -1. (a) (1 point) Determine the interval(s) where the function is increasing / decreasing, if any. (b) (1 point) Determine the interval(s) where the graph of the function is concave up / down, if any. (c) (1 point) Determine the value(s) of x where this function attains a relative (local) maximum / minimum, if any. (d) (1 point) Determine the value(s) of x where the graph of this function has an inflection point, if any. (e) (2 points) Sketch the graph of this function. You are just asked to find the intervals (in (a) and (b)) or the values of x (in (c) and (d)) or the graph of f(x) (in (e)). No explanations are needed. Hint: it may help you to write a table with signs of f' and f"